To answer your question: I believe that it isn't easy to get an invitation letter anymore because of too many people who wouldn't return. Also there are criterias for the sponsor of the invitation letter which makes the person entirely responsible for you which many are not willing to do. Also they must be working for at least 3 years and have 20,000$ in their account. You must also buy an insurance in case anything happened to you.
I worked in a lawyer's office and my invitation letter to a friend to attend my business associates wedding..was refused and he answered all the critirias as well as I.
The best is to try to get a tourist visa and still you have to answer to critirias, so find out beforehand what they are in your country.